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On the C1 non-integrability of differential systems via periodic orbits

Published online by Cambridge University Press:  06 April 2011

JAUME LLIBRE  and
CLÀUDIA VALLS
JAUME LLIBRE
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain email: [email protected]
CLÀUDIA VALLS
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1049-001, Lisboa, Portugal email: [email protected]
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Abstract

We go back to the results of Poincaré [Poincare, H (1891) Sur lintegration des equations differentielles du premier ordre et du premier degre I and II, Rendiconti del circolo matematico di Palermo5, 161–191] on the multipliers of a periodic orbit for proving the C1 non-integrability of differential systems. We apply these results to Lorenz, Rossler and Michelson systems, among others.

Keywords

C1 integrabilitydifferential systemsperiodic orbits
Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 4 , August 2011 , pp. 381 - 391
Copyright
Copyright © Cambridge University Press 2011

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